What is the angular velocity of an aircraft passing overhead at 900 km/h?

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Homework Help Overview

The problem involves calculating the angular velocity of an aircraft passing overhead at a speed of 900 km/h and an altitude of 10,000 m. The context is centered around concepts of angular motion and the relationship between linear speed and angular velocity.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to approach the problem and questions whether angular velocity exists for a straight-flying aircraft. Some participants suggest analyzing the angle formed between the observer's line of sight and the vertical as the aircraft moves, proposing to derive an expression for this angle over time.

Discussion Status

Participants are exploring different interpretations of the problem, with some providing guidance on how to relate the angle to time and angular velocity. There is a suggestion to convert the aircraft's speed to consistent units, indicating a productive direction in the discussion.

Contextual Notes

One participant notes the importance of unit consistency, specifically converting the aircraft's speed from km/h to m/s, which may affect the calculations. The original poster is also grappling with the implications of the aircraft's straight flight path on the concept of angular velocity.

haxan7
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Homework Statement


An aircraft passes directly over you with a speed of 900 km/h at an altitude of 10,000 m. What is the angular velocity of the aircraft (relative to you) when directly overhead? Three minutes later?

Homework Equations


Where were studying center of mass and Moment of inertia.

The Attempt at a Solution


No idea, how to approach this question, Aircraft is flying straight, will there even by any angular velocity?
 
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Draw a straight line from your eye to the aircraft. It changes direction as the aircraft flies over you, does not it? The line encloses an angle alpha with the vertical. Find the expression for this angle in terms of time. The angular velocity is the time derivative of the angle.

ehild
 
ehild said:
Draw a straight line from your eye to the aircraft. It changes direction as the aircraft flies over you, does not it? The line encloses an angle alpha with the vertical. Find the expression for this angle in terms of time. The angular velocity is the time derivative of the angle.

ehild

Speed = 900km/hour
tan(α)=900t/10000
α=arctan(900t/10000)

Derivative is 900/(10000+81 t^2)
If i put t = 0 and t = 3/60, will i get the correct answer? I don't think so, Help me.
 
Last edited:
Do not mix units. Convert the speed of the aircraft to m/s.

ehild
 

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